Question 1

Given the quadratic function $f(x) = 2x^2 + 3x - 7$, what is the axis of symmetry?

Accepted Answer

$x = -\frac{3}{2}$

Question 2

For the quadratic function $f(x) = -x^2 + 4x - 5$, what is the vertex?

Accepted Answer

$(2, -1)$

Question 3

Which of the following describes the direction in which the parabola $f(x) = -2(x-1)^2 + 3$ opens?

Accepted Answer

Downward

Question 4

What is the range of the function $f(x) = -x^2 + 2x + 3$?

Accepted Answer

$(-\infty, 4]$

Question 5

If a quadratic function is written in vertex form $f(x) = a(x-h)^2 + k$, what does the value of $a$ determine?

Accepted Answer

The direction and width of the parabola

Question 6

Given $f(x) = 3(x+2)^2 - 5$, what is the minimum or maximum value of the function?

Accepted Answer

Minimum at $y = -5$

Question 7

Which transformation occurs when the function $f(x) = (x-4)^2 + 2$ is compared to $f(x) = x^2$?

Accepted Answer

Shift right 4 units and up 2 units

Question 8

A ball is thrown upward and its height in meters after $t$ seconds is given by $h(t) = -5t^2 + 20t + 2$. What is the maximum height reached by the ball?

Accepted Answer

$22$ meters

Question 9

Convert the quadratic function $f(x) = x^2 - 6x + 5$ to vertex form.

Accepted Answer

$f(x) = (x-3)^2 - 4$

Question 10

For the function $f(x) = -2x^2 + 8x - 6$, over which interval is the function increasing?

Accepted Answer

$(-\infty, 2]$

Question 11

What is the domain of any quadratic function?

Accepted Answer

$(-\infty, \infty)$

Question 12

Which of the following is the correct formula for the axis of symmetry of $f(x) = ax^2 + bx + c$?

Accepted Answer

$x = -\frac{b}{2a}$

Question 13

A parabola models the path of a thrown object. If the vertex is at $(3, 7)$, what does this point represent in the context of the object's motion?

Accepted Answer

The highest point reached by the object

Question 14

Given $f(x) = 2x^2 - 8x + 6$, what is the y-intercept?

Accepted Answer

$6$

Question 15

Which of the following quadratic functions has a vertex at $(1, -2)$?

Accepted Answer

$f(x) = (x-1)^2 - 2$

Question 16

If $f(x) = -3(x+2)^2 + 4$, what is the domain and range of $f(x)$?

Accepted Answer

Domain: $(-\infty, \infty)$, Range: $(-\infty, 4]$

Question 17

Which method can be used to convert a quadratic function from standard form to vertex form?

Accepted Answer

Completing the square

Question 18

For $f(x) = x^2 - 4x + 7$, what is the vertex?

Accepted Answer

$(2, 3)$

Question 19

If $f(x) = -x^2 + 6x - 8$, over which interval is the function decreasing?

Accepted Answer

$[3, \infty)$

Question 20

A company models its profit with $P(x) = -2x^2 + 12x - 16$, where $x$ is the number of items sold. What is the maximum profit?

Accepted Answer

$52$

Quadratic Functions: Properties, Vertex Form, and Graphing Techniques

Study Guide - Practice Questions

Study Guide - Flashcards